Computational Fluid Dynamics (CFD) is a powerful tool which can help with the geometry optimization of continuous milli-scale reactors, which often are highly complex devices. Attempting to perform this optimization by manually modifying and testing geometry configurations can however be tedious and computationally inefficient. Addressing this problem, we present a framework in which the CFD software COMSOL Multiphysics is coupled with the multi-objective Bayesian Optimization algorithm TSEMO (Thompson sampling efficient multiobjective optimization), implemented in MATLAB. The mixing element geometry of a Miprowa Lab millireactor is parameterized, and the framework automatically executes CFD simulations to minimize areas of stagnating flow and maximize the mixing performance. The framework is able to find Pareto-optimal reactor variations, and can easily be adapted for other devices and objectives.

Hybrid modelling, i.e., the combination of data-driven modelling with mechanistic model components, reduces the data demand and enables extrapolation of data-driven models. However, building, training and evaluation of hybrid models is cumbersome with current frameworks. We developed HybridML, an open-source modeling platform, in which hybrid models can be trained, i.e., combinations of artificial neural networks, arithmetic expressions, and differential equations. We employ TensorFlow for artificial neural network training and Casadi to integrate ordinary differential equations and provide gradients of differential model equations enabling continuous time representations. HybridML provides also a JSON interface for the model development. We apply HybridML to an industrial case study, in which the trained model is used to predict drug concentrations over time, based on physiological information about the patients. To demonstrate its versatility, we also present a nonlinear application, where HybridML is used to model the spread of the COVID-19 pandemic in German federal states based on the state's socio-economic attributes.

Pressure swing adsorption (PSA) is an energy-efficient technology for gas separation, while the multiobjective optimization of PSA is a challenging task. To tackle this, we propose a hybrid optimization framework (TSEMO + DyOS), which integrates two steps. In the first step, a Bayesian stochastic multiobjective optimization algorithm (i.e., TSEMO) searches the entire decision space and identifies an approximated Pareto front within a small number of simulations. Within TSEMO, Gaussian process (GP) surrogate models are trained to approximate the original full process models. In the second step, a gradient-based deterministic algorithm (i.e., DyOS) is initialized at the approximated Pareto front to further refine the solutions until local optimality. Therein, the full process model is used in the optimization. The proposed hybrid framework is efficient, because it benefits from the coarse-to-fine function evaluations and stochastic-to-deterministic searching strategy. When the result is far away from the optima, TSEMO can efficiently approximate a trade-off curve as good as a commonly used evolutional algorithm, i.e., Nondominated Sorting Genetic Algorithm II (NSGA-II), while TSEMO only uses around 1/16th of CPU time of NSGA-II. This is because the GP-based surrogate model is utilized for function evaluations in the initial coarse search. When the result is near the optima, the searching efficiency of TSEMO dramatically decreases, while DyOS can accelerate the searching efficiency by over 10 times. This is because, in the proximity of optima, the exploitation capacity of DyOS is significantly higher than that of TSEMO.

Extensive literature has considered reduced, but still highly accurate, nonlinear dynamic process models, particularly for distillation columns. Nevertheless, there is a need for continuing research in this field. Herein, opportunities from the integration of machine learning into existing reduction approaches are discussed. First, key concepts for dynamic model reduction and their limitations are briefly reviewed. Afterwards, promising model structures for reduced hybrid mechanistic/data-driven models are outlined. Finally, crucial future challenges as well as promising research perspectives are presented.